2. A simple type of graphical
projection
Used for producing pictorial, 2d images of 3d objects.
3. Oblique projection
A parallel projection
Projects a 3d image by the intersection of the parallel rays which is
known as projectors.
Parallel lines of the source object produces a parallel lines in the
projected images.
the projectors intersects the projection in oblique angle to produce
the projected image.
Parallel projection of the point(x,y,z) on the xy plane is (x+az,y+bz,0)
4. Types of parallel projection
When a=b=0, the projection is said to be orthographic or orthogonal
If not the projection is oblique
5. More about the parallel projection
Crudest 3d drawing but easy to master.
Oblique is not really 3d system but 2d view of an object with ‘forced
depth’.
Oblique is rarely used as it is unconvincing to the eye.
6. Oblique peojection
Angles displayed among the axes
Foreshortening factors or scales are arbitrary
Length along the x and y direction are preserved
Length along the z axis are drawn at an angle using a reduction
factor
7. Cavalier projection
Also known as high view point
Length along the z axis remain unscaled
Easy to draw
Y axis is drawn diagonally making an angle of 30 or 45 degree with x
axis.
X and z are perpendicular and length on these axes are 1:1 scaled
8. Cabinet projection
Used by furniture industry
One face of the object is parallel to the viewing plane
Third axis is projected at angle 30 or 45 degree
The projection length of the receding lines are half
9. Mathematical formula
A projected point has the following transformation formula
X = X + 0.5 * Z * cos()
Y = Y + 0.5 * Z * sin()
Z=0
is the mentioned angle
